On diversity and stability of unit bases for the Euclidean metric

DOI10.1007/s00022-009-0010-xzbMath1211.05087OpenAlexW2088558344MaRDI QIDQ1037202

Alexandr V. Kuzminykh

Publication date: 13 November 2009

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-009-0010-x

zbMATH Keywords

homomorphismrigidincomparableunit distance grapheuclidean metric

Mathematics Subject Classification ID

Distance in graphs (05C12) General theory of distance geometry (51K05) Graph representations (geometric and intersection representations, etc.) (05C62)

Cites Work

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• Imbeddability of recursively presented inverse semigroups into finitely presented ones
• An elementary proof of the theorem of Beckman and Quarles
• On mappings preserving the distance 1 only in a finite number of directions
• Mappings preserving unit distance
• On binary relations without non-identical endomorphisms
• Discrete versions of the Beckman-Quarles theorem
• Symmetric relations (undirected graphs) with given semigroups
• Functions That Preserve Unit Distance
• On Isometries of Euclidean Spaces

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